{"id":"W1973310611","doi":"10.1007/s10958-010-0093-9","title":"Well-defined solvability and spectral properties of abstract hyperbolic equations with aftereffect","year":2010,"lang":"en","type":"article","venue":"Journal of Mathematical Sciences","topic":"Stability and Controllability of Differential Equations","field":"Engineering","cited_by":14,"is_retracted":false,"has_abstract":false,"ca_institutions":"York University","funders":"Russian Foundation for Basic Research","keywords":"Mathematics; Sobolev space; Mathematical analysis; Hyperbolic partial differential equation; Hilbert space; Operator (biology); Principal part; Boundary value problem; Heat equation; Integral equation; Volterra integral equation; Differential equation","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008520089,0.00008433363,0.0002520976,0.0000587826,0.00006937055,0.00005049564,0.0001497009,0.00003823846,0.0001748183],"category_scores_gemma":[0.0006094617,0.00004840805,0.0000622366,0.0001255045,0.0005644862,0.0002162505,0.00001148783,0.0001798863,0.000003554989],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00000958528,"about_ca_system_score_gemma":0.00004994807,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005770458,"about_ca_topic_score_gemma":0.0000714416,"domain_scores_codex":[0.9990814,0.00002081685,0.000378175,0.00007754607,0.0003111201,0.0001309478],"domain_scores_gemma":[0.9992092,0.0004367753,0.0000891305,0.0001002114,0.00008521467,0.00007949607],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"bench_or_experimental","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0002188273,0.001334387,0.01442275,0.001777158,0.000233042,0.000003730123,0.004639511,0.004668089,0.9008514,0.057881,0.00002047584,0.0139496],"study_design_scores_gemma":[0.003431886,0.002897772,0.2924017,0.0009572586,0.000479048,0.0002383929,0.002640852,0.1819107,0.161037,0.3529743,0.00007595688,0.000955151],"study_design_candidate":"bench_or_experimental","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9952518,0.00006691906,0.00297755,0.0003713596,0.00006544529,0.0001176512,0.000001345761,0.00001484532,0.001133024],"genre_scores_gemma":[0.995783,0.000003621349,0.004162083,0.000004200782,0.00003716134,0.00000300016,4.781868e-8,0.000003595357,0.000003347743],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.7398145,"threshold_uncertainty_score":0.2079873,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01966041339291084,"score_gpt":0.2255098052154102,"score_spread":0.2058493918224994,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}